Volumetric strainmeters are often used to monitor changes in strain in the earth's interior. Volumetric strainmeters are considered to be the most sensitive of sensors used to measure small changes in subterranean stress or strain. A typical strainmeter 100 shown in FIG. 1 may be inserted into a subterranean formation to monitor tectonic stress. The strainmeter 100 includes a housing 102 enclosing a chamber 104 filled with a fluid, a capillary tube 106, and a differential transformer 108 connected to the capillary tube 106. The capillary tube 104 is in fluid communication with the chamber 104. The differential transformer 108 measures the volume of fluid that comes out of or is displaced from the chamber 104 when tectonic stress compresses and deforms the chamber 104.
However, if the volume of fluid displaced from the chamber 104 exceeds the capacity of the differential transformer 108, a quantum-metered overcapacity relief valve 110 in fluid communication with the chamber 104 opens and allows fluid flow from the chamber 104 into an overcapacity chamber 112 filled with Argon gas. The volume of fluid that may enter the overcapacity chamber 112 is constant or quantized, and the strainmeter counts and records the number of times an overcapacity condition occurs. Therefore, the total amount of fluid displaced from the chamber 104 into the overcapacity chamber 112 is readily determined.
The fluid volume V of the chamber 104 is expressed as:
                    V        =                              π            ⁢                                                  ⁢                          D              2                        ⁢            L                    4                                    (        1        )            where:    D is the internal diameter of the chamber; and    L is the internal length of the chamber.
The volumetric change ΔV is therefore:
                              Δ          ⁢                                          ⁢          V                =                                            π              ⁢                                                          ⁢              L                        4                    ⁢                      (                                          D                2                2                            -                              D                1                2                                      )                                              (        2        )            for a diameter change from D1 to D2 due to strain. Accordingly, the sensitivity of the strainmeter 100 is governed by its diameter and length, and strain can be determined by measuring the volume of fluid displaced from the chamber 104.
The fluid in the chamber 104 is often silicon oil. The thermal expansion coefficient α of silicon oil is approximately 9.5×10−4. Therefore, strain due to changes in temperature is:
                                          Δ            ⁢                                                  ⁢            V                    V                =                  α          ⁢                                          ⁢          Δ          ⁢                                          ⁢          T          ⁢                                          ⁢                      (                                                                               °                                ⁢                C                            .                        )                                              (        3        )            However, to measure volumetric strain on the order of 10−12 (the resolution commonly sought for subterranean oilfield applications) the required stability of the temperature should be less than:
                              Δ          ⁢                                          ⁢          T                =                                            10                              -                12                                                    9.5              ⨯                              10                                  -                  4                                                              ≅                                    10                              -                9                                      ⁢                                                  ⁢                          (                                                                                         °                                    ⁢                  C                                .                            )                                                          (        4        )            
It may be difficult or impossible to maintain temperature stability to 10−9 (° C.), and it may not even be possible to verify that the temperature at the strainmeter is within such an order. Therefore, the strainmeter 100 may be equipped with a thermocouple 114 as shown in FIG. 1 to measure the fluid temperature and compensate for fluid thermal expansion due to temperature variations. The highest resolution currently available for temperature measurement is about 1/1000° C. This corresponds to a strain resolution on the order of 10−6. However, for long term subterranean monitoring, the best resolution available for temperature measurement is about 1/100° C. and many orders of magnitude too low to provide strain measurement on the order of 10−9.
Moreover, even if temperature could be measured with enough accuracy to compensate for thermal fluid expansion for strain measurements on the order of 10−9, the thermocouple 114 only measures the temperature of the fluid locally. Temperature may be distributed throughout the chamber 104 while and the measured temperature is the temperature at the thermocouple. Thermal expansion of the fluid represents the true average temperature throughout the chamber 104 or the integration of thermal expansion in the whole fluid volume. Accordingly, it is important to reduce temperature sensitivity of volumetric strainmeters and further separate temperature dependency from stress changes.
The present invention is direct to overcoming, or at least reducing the effects of, one or more of the problems presented above.